High-order methods for systems of fractional ordinary differential equations and their application to time-fractional diffusion equations

DOI10.1007/s11786-019-00448-xOpenAlexW3000544683WikidataQ126347451 ScholiaQ126347451MaRDI QIDQ2071517

Magda Rebelo, Maria Luísa Morgado, Neville J. Ford, Luis L. Ferrás

Publication date: 28 January 2022

Published in: Mathematics in Computer Science (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/1822/66733

zbMATH Keywords

method of linesCaputo derivativefractional diffusionnonpolynomial collocation methodpolynomial collocation method

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integro-partial differential equations (45K05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Stability and convergence of numerical methods for ordinary differential equations (65L20)

Related Items (4)

Non-linear system of multi-order fractional differential equations: theoretical analysis and a robust fractional Galerkin implementation ⋮ High‐order schemes and their error analysis for generalized variable coefficients fractional reaction–diffusion equations ⋮ B-spline collocation discretizations of Caputo and Riemann-Liouville derivatives: a matrix comparison ⋮ High-order methods for systems of fractional ordinary differential equations and their application to time-fractional diffusion equations

Cites Work

• Unnamed Item
• Moving finite element methods for time fractional partial differential equations
• A box-type scheme for fractional sub-diffusion equation with Neumann boundary conditions
• A compact finite difference scheme for the fractional sub-diffusion equations
• Compact finite difference method for the fractional diffusion equation
• Some aspects of fractional diffusion equations of single and distributed order
• Some uniqueness and existence results for the initial-boundary-value problems for the generalized time-fractional diffusion equation
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Implicit finite difference approximation for time fractional diffusion equations
• Fractals and fractional calculus in continuum mechanics
• An algorithm for the numerical solution of differential equations of fractional order
• An approach to construct higher order time discretisation schemes for time fractional partial differential equations with nonsmooth data
• The accuracy and stability of an implicit solution method for the fractional diffusion equation
• Time fractional diffusion: A discrete random walk approach
• A time-space collocation spectral approximation for a class of time fractional differential equations
• High-order methods for systems of fractional ordinary differential equations and their application to time-fractional diffusion equations
• Nonpolynomial collocation approximation of solutions to fractional differential equations
• Finite difference/spectral approximations for the time-fractional diffusion equation
• Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term
• Volterra integral equations and fractional calculus: do neighboring solutions intersect?
• A Fourier method for the fractional diffusion equation describing sub-diffusion
• Comparison of numerical methods for fractional differential equations
• Finite difference methods and a Fourier analysis for the fractional reaction-subdiffusion equation
• Weighted average finite difference methods for fractional diffusion equations
• Pitfalls in fast numerical solvers for fractional differential equations
• A semi-discrete finite element method for a class of time-fractional diffusion equations
• Maximum principle and its application for the time-fractional diffusion equations
• Fractional boundary value problems: Analysis and numerical methods
• Fractional diffusion and wave equations
• The fractional diffusion equation
• A Hybrid Collocation Method for Volterra Integral Equations with Weakly Singular Kernels
• An Explicit Finite Difference Method and a New von Neumann-Type Stability Analysis for Fractional Diffusion Equations
• Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
• Analysis of fractional differential equations

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